DM FUNCTION AND MICCHELLỈ̉S THEOREM
A function 𝑓 is said to be a DM function on [0,∞) if 𝑓 is continuous function on [0,∞) and its derivatives is continuous on (0,∞) and the first derivative, 𝑓′, is a completely monotone (CM) function. This thesis discusses DM...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/22528 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A function 𝑓 is said to be a DM function on [0,∞) if 𝑓 is continuous function on [0,∞) and its derivatives is continuous on (0,∞) and the first derivative, 𝑓′, is a completely monotone (CM) function. This thesis discusses DM functions and their application in the problem of interpolation based on Micchelli’s Theorem. Micchelli’s Theorem states that for a DM function 𝑓, the matrix [𝐴𝑖𝑗]=𝑓(‖𝑥𝑖−𝑥𝑗‖2) is nonsingular. Besides the problem of interpolation, this thesis also discusses the application of DM functions in the problem of embedding a finite dimensional quasi-metric space into Euclidean space. |
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